Abstract
In theoretical chemistry, fuzzy molecular graphs can be used to model chemical molecular structures with uncertainty information, where the vertex membership function and edge membership function describe the uncertainty of atoms and chemical bonds respectively. This paper studies chemical topological index of bipolar cubic fuzzy graphs. The new concepts and theorems are given in terms of graph theory and fuzzy set theory approaches and several theoretical conclusions on bipolar Wiener index of bipolar cubic fuzzy graphs are determined. Furthermore, we apply it in chemical science and calculate the bipolar Wiener index of dimethyltryptamine and hallucinogen which are modelled by bipolar cubic fuzzy graphs.